Answer to Question #288431 in Algebra for Amrita

Question

f(x)= x^4 +8x^3+16x^2

g(x) = -4x^2 -16x +5

using algebraic method, find the points of intersection of the graphs f(x) and g(x).

which of the solutions are reflected on the graphs

Answer 1

At point of intersection

$f(x)=g(x)$

$x^4+8x^3+16x^2=-4x^2-16x+5$

$x^4+8x^3+20x^2+16x-5=0$

Factorizing

$(x-0.23606)(x+4.23606)(x^2+4x+5)=0$

Points of intersection are:

x=0.23606

x=-4.23606

This two are for $x\in \reals$

Imaginary points of intersection are:

x={-2-i}

x={-2+i}